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Simplifying (2x + 3)(x + 2) = 46 Reorder the terms: (3 + 2x)(x + 2) = 46 Reorder the terms: (3 + 2x)(2 + x) = 46 Multiply (3 + 2x) * (2 + x) (3(2 + x) + 2x * (2 + x)) = 46 ((2 * 3 + x * 3) + 2x * (2 + x)) = 46 ((6 + 3x) + 2x * (2 + x)) = 46 (6 + 3x + (2 * 2x + x * 2x)) = 46 (6 + 3x + (4x + 2x2)) = 46 Combine like terms: 3x + 4x = 7x (6 + 7x + 2x2) = 46 Solving 6 + 7x + 2x2 = 46 Solving for variable 'x'. Reorder the terms: 6 + -46 + 7x + 2x2 = 46 + -46 Combine like terms: 6 + -46 = -40 -40 + 7x + 2x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -40 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20 + 3.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 3.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 3.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 3.5x + x2 = 0 + 20 3.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 3.5x + x2 = 20 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 20 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 20 + 3.0625 Combine like terms: 20 + 3.0625 = 23.0625 3.0625 + 3.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + 1.75) equal to 4.802343178 and -4.802343178.Subproblem 1
x + 1.75 = 4.802343178 Simplifying x + 1.75 = 4.802343178 Reorder the terms: 1.75 + x = 4.802343178 Solving 1.75 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.802343178 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.802343178 + -1.75 x = 4.802343178 + -1.75 Combine like terms: 4.802343178 + -1.75 = 3.052343178 x = 3.052343178 Simplifying x = 3.052343178Subproblem 2
x + 1.75 = -4.802343178 Simplifying x + 1.75 = -4.802343178 Reorder the terms: 1.75 + x = -4.802343178 Solving 1.75 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.802343178 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.802343178 + -1.75 x = -4.802343178 + -1.75 Combine like terms: -4.802343178 + -1.75 = -6.552343178 x = -6.552343178 Simplifying x = -6.552343178Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.052343178, -6.552343178}
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